Deep Learning Methods for Adjusting Global MFD Speed Estimations to Local Link Configurations

TL;DR

The work tackles the mismatch between Macroscopic Fundamental Diagram (MFD) models and per-link traffic states by introducing a Local Correction Factor (LCF) learned via a deep graph framework that fuses spatial (GAT) and temporal (GRU) embeddings, augmented by network partitioning. The model estimates per-link speeds as $V_i^t = V_{\text{mean}}^{t} + \text{LCF}_i^t$, where $\text{LCF}^t = f_{\text{LCF}}(G; V_{\text{mean}}^{t})$, enabling granular, link-level corrections while preserving MFD efficiency. The architecture comprises data preprocessing, spatial embedding with multi-head GATs, temporal embedding with GRUs, and a final speed estimator, trained on SaF-based Barcelona simulations with diverse OD and bus-lane configurations. Results show substantial improvements over baselines, especially with network partitioning (GAT-GRU-P), achieving about 84% reduction in path-travel-time error relative to MFD and robust performance across demand levels, demonstrating practical applicability for rapid, large-scale traffic optimization.

Abstract

In large-scale traffic optimization, models based on Macroscopic Fundamental Diagram (MFD) are recognized for their efficiency in broad network analyses. However, they fail to reflect variations in the individual traffic status of each road link, leading to a gap in detailed traffic optimization and analysis. To address the limitation, this study introduces a Local Correction Factor (LCF) that represents local speed deviations between the actual link speed and the MFD average speed based on the link configuration. The LCF is calculated using a deep learning function that takes as inputs the average speed from the MFD and the road network configuration. Our framework integrates Graph Attention Networks (GATs) with Gated Recurrent Units (GRUs) to capture both the spatial configurations and temporal correlations within the network. Coupled with a strategic network partitioning method, our model enhances the precision of link-level traffic speed estimations while preserving the computational advantages of aggregate models. In our experiments, we evaluate the proposed LCF across various urban traffic scenarios, including different levels of origin-destination trip demand and distribution, as well as diverse road configurations. The results demonstrate the robust adaptability and effectiveness of the proposed model. Furthermore, we validate the practicality of our model by calculating the travel time of each randomly generated path, achieving an average error reduction of approximately 84% relative to MFD-based results.

Figures (13)

• Figure 1: Illustration of additional road link attributes
• Figure 2: The model architecture of proposed LCF
• Figure 3: The architecture of the GATs
• Figure 4: The model architecture of GRU
• Figure 5: Road network of Barcelona with candidate bus links